Since \(z^{-(g-m_0)}\Psi (x;z)\)  is invariant when \(p\)  goes round \(\epsilon _i\) , \(\delta _i\)  cycles, the expansion coefficients in \(x_1,x_2,\dots \)  of \(z^{-(g-m_0)}\Psi (x;z)\theta (\Gamma x+e\,|\,\Omega )\)  are elements of \(H^0(X,{\cal O}(D+\ast \infty _+))\) . Therefore \(\tau (x)\)  coincides with \(\tau \big (x;\tilde{\xi }(D)\big )\)  up to a constant multiple (see [1]}).
